Step 1 — Daily Log Returns

For each pair of consecutive closing prices, compute the natural log return:

r(t) = ln( Close(t) / Close(t-1) )

This gives 9 return values from 10 closing prices.

Step 2 — Daily Volatility (σ)

Daily volatility is the sample standard deviation of the log returns:

σ_daily = √[ Σ(r(t) − r̄)² / (n − 1) ]

where r̄ is the mean of all log returns and n is the number of returns (9 for 10 prices).

Step 3 — Scaling to Weekly & Annual

Volatility scales with the square root of time:

σ_weekly = σ_daily × √5     (5 trading days per week) σ_annual = σ_daily × √252   (252 trading days per year)

Step 4 — Daily Price Range

The expected intraday price range is derived from daily volatility:

Price Range = σ_daily × Previous Close Price

This represents the expected ±1σ movement for the day.

Reference — Annual Volatility (NSE / SmartFinance method)

Daily Vol (%) = σ_daily × 100 Annual Vol (%) = σ_daily × √252 × 100

Matches the output on smartfinancein.com and pivottrading.co.in volatility calculators.

The Core Difference

The Average True Range (ATR) measures the average of each session’s full price swing — from high to low, including any overnight gap — smoothed over a period (typically 14 days). It tells you how wide each candle has been in absolute price terms.

The Gann volatility method uses only the closing price series, computing the standard deviation of log returns (close-to-close percentage moves). It tells you how much the market has drifted per session as a percentage of price — a fundamentally different quantity.

Reason 1 — Gann’s Theory is Built on Closing Prices

W.D. Gann treated the closing price as the single most important price of the day — the point where the market “agrees” on value after the session’s noise has settled. His angle calculations, time cycles, and squaring-of-price methods all anchor to closing values, not intraday extremes. Using ATR (which is driven by intraday highs and lows) would import data that Gann’s framework deliberately ignores.

Reason 2 — Percentage Volatility Scales Cleanly Across Timeframes

Because log-return volatility is dimensionless (expressed as a fraction of price), it obeys the square-root-of-time rule precisely:

σ_weekly = σ_daily × √5     σ_annual = σ_daily × √252

ATR is expressed in absolute price points, not percentages. A Nifty ATR of 120 points means something very different at 10,000 than at 24,000. It cannot be annualised or scaled across timeframes without first converting to a percentage — at which point you are replicating the log-return method anyway.

Reason 3 — 10 Days is the Established Gann Convention

Indian Gann practitioners (as documented on smartfinancein.com and pivottrading.co.in) use 10 closing prices to balance two needs: enough data to smooth outliers, but recent enough to reflect the current volatility regime. ATR’s default 14-period window introduces a slight lag and weights each day’s full intraday range equally — it cannot distinguish between a quiet close after a wild intraday swing and a genuinely volatile session.

Reason 4 — Price Range from σ is Proportional to Price

The expected daily range in Gann methodology is:

Price Range = σ_daily × Previous Close

This automatically adjusts the absolute range as the instrument’s price changes — a natural property of percentage volatility. ATR does not self-adjust; as price rises or falls significantly, ATR needs manual re-calibration. For Gann angles, which are fundamentally about price × time geometry, proportional scaling to current price is essential.

Summary Comparison

Feature	Gann Method (10-day σ)	ATR (14-day default)
Input data	Closing prices only	High, Low, Prev Close (OHLC)
Output unit	Percentage (dimensionless)	Absolute price points
Captures intraday range?	No — by design	Yes
Scales across timeframes?	Yes — via √T rule	Not directly
Self-adjusts with price level?	Yes	No
Aligns with Gann’s theory?	Yes — close-price anchored	No — uses intraday extremes
Smoothing method	Sample standard deviation	Wilder’s exponential smoothing
Annualisation	Straightforward (× √252)	Not meaningful without conversion

In short: ATR is the right tool when you need to size stops based on recent intraday swings. The 10-day closing-price σ is the right tool when working within Gann’s framework — projecting daily and annual price envelopes anchored to closing-price geometry and scaling proportionally with the instrument’s current level.